Gevrey-smoothness of lower dimensional hyperbolic invariant tori for nearly integrable symplectic mappings

This paper develops a new KAM theorem for a class of lower dimensional elliptic invariant tori of nearly integrable symplectic mappings with generating functions but without assuming any nondegenerate condition.

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Lower dimensional invariant tori with prescribed frequency for nonlinear wave equation

Journal of Differential Equations ◽

10.1016/j.jde.2010.04.003 ◽

2010 ◽

Vol 249 (11) ◽

pp. 2796-2821 ◽

Cited By ~ 8

Author(s):

Jiansheng Geng ◽

Xiufang Ren

Keyword(s):

Wave Equation ◽

Nonlinear Wave ◽

Nonlinear Wave Equation ◽

Invariant Tori ◽

Lower Dimensional Invariant Tori ◽

Lower Dimensional

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Lower dimensional invariant tori for quasiperiodically forced circle diffeomorphisms

Journal of Differential Equations ◽

10.1016/j.jde.2012.05.005 ◽

2012 ◽

Vol 253 (5) ◽

pp. 1489-1543 ◽

Cited By ~ 1

Author(s):

Jing Wang

Keyword(s):

Invariant Tori ◽

Lower Dimensional Invariant Tori ◽

Circle Diffeomorphisms ◽

Lower Dimensional

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Persistence of lower dimensional degenerate invariant tori with prescribed frequencies in Hamiltonian systems with small parameter

Nonlinearity ◽

10.1088/1361-6544/ac2c91 ◽

2021 ◽

Vol 34 (12) ◽

pp. 8192-8247

Author(s):

Junxiang Xu

Keyword(s):

Small Parameter ◽

Hamiltonian Systems ◽

Invariant Tori ◽

Lower Dimensional

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Lower Dimensional Invariant Tori in the Regions of Instability for Nearly Integrable Hamiltonian Systems

Communications in Mathematical Physics ◽

10.1007/s002200050618 ◽

1999 ◽

Vol 203 (2) ◽

pp. 385-419 ◽

Cited By ~ 15

Author(s):

Chong-Qing Cheng

Keyword(s):

Hamiltonian Systems ◽

Invariant Tori ◽

Integrable Hamiltonian Systems ◽

Lower Dimensional Invariant Tori ◽

Nearly Integrable Hamiltonian Systems ◽

Lower Dimensional

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Persistence of lower dimensional invariant tori for nearly integrable Hamiltonian systems

Nonlinear Analysis ◽

10.1016/s0362-546x(01)00904-x ◽

2003 ◽

Vol 52 (2) ◽

pp. 383-403 ◽

Cited By ~ 2

Author(s):

Junxiang Xu

Keyword(s):

Hamiltonian Systems ◽

Invariant Tori ◽

Integrable Hamiltonian Systems ◽

Lower Dimensional Invariant Tori ◽

Nearly Integrable Hamiltonian Systems ◽

Lower Dimensional

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Persistence of Elliptic Lower Dimensional Invariant Tori for Small Perturbation of Degenerate Integrable Hamiltonian Systems

Journal of Mathematical Analysis and Applications ◽

10.1006/jmaa.1997.5313 ◽

1997 ◽

Vol 208 (2) ◽

pp. 372-387 ◽

Cited By ~ 6

Author(s):

Xu Junxiang

Keyword(s):

Hamiltonian Systems ◽

Small Perturbation ◽

Invariant Tori ◽

Integrable Hamiltonian Systems ◽

Lower Dimensional Invariant Tori ◽

Lower Dimensional

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Persistence of Degenerate Lower Dimensional Invariant Tori in Reversible Systems with Bruno Non-degeneracy Conditions

Qualitative Theory of Dynamical Systems ◽

10.1007/s12346-020-00439-5 ◽

2021 ◽

Vol 20 (1) ◽

Author(s):

Xiaomei Yang ◽

Junxiang Xu

Keyword(s):

Invariant Tori ◽

Reversible Systems ◽

Lower Dimensional Invariant Tori ◽

Lower Dimensional

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The hyperbolic invariant tori of symplectic mappings

Nonlinear Analysis ◽

10.1016/j.na.2006.10.035 ◽

2008 ◽

Vol 68 (1) ◽

pp. 109-126 ◽

Cited By ~ 8

Author(s):

Wenzhuang Zhu ◽

Baifeng Liu ◽

Zhenxin Liu

Keyword(s):

Invariant Tori ◽

Symplectic Mappings

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